For now it's only a speculation, but, from their behavior and investigation on Mary and Masumi, it's very probably that the mysterious man with respirator is Yasuharu Haneda, Kohji Haneda's father, who hated the Japanese police due his son's murder case's irresolution, and his driver Tsutomu Akai in disguise, who are friends. Then, Renya Karasuma is very probably the old man looking like a Tengu. In any case, we must wait the author's resolution.